📚 Year 8 OCR Statistics: Unit Test Mock Paper Analysis | Year 8 OCR 统计：单元测试模拟卷解析
This article walks you through a typical Year 8 OCR Statistics unit test by analysing a mock paper. Each section tackles a key question type you are likely to meet, showing you exactly how marks are earned. Working through these worked examples will help you deepen your understanding of averages, charts, probability, data collection and correlation.
本文通过解析一份模拟试卷，带你梳理典型的 Year 8 OCR 统计单元测试。每一节聚焦一种你可能遇到的核心题型，清楚地展示如何拿到分数。跟着这些详细解析一起练习，能帮你加深对平均数、图表、概率、数据收集和相关性等内容的理解。
1. Mean, Median, Mode and Range from a List | 从列表求平均数、中位数、众数和范围
The scores of seven students in a quick mental‑maths test are recorded below.
七名学生在速算小测中的得分记录如下。
Data set: 8, 12, 9, 12, 10, 12, 11
数据集：8, 12, 9, 12, 10, 12, 11
To find the mean, add all the values together and divide by how many values there are. The total is 8 + 12 + 9 + 12 + 10 + 12 + 11 = 74, so the mean is 74 ÷ 7 ≈ 10.6 (to 1 d.p.).
求平均数时，先将所有数据相加，再除以数据的个数。总和为 8 + 12 + 9 + 12 + 10 + 12 + 11 = 74，因此平均数为 74 ÷ 7 ≈ 10.6（保留一位小数）。
For the median, put the numbers in order: 8, 9, 10, 11, 12, 12, 12. The middle value is the 4th number, so the median is 11.
求中位数时，把数据按大小排列：8, 9, 10, 11, 12, 12, 12。中间是第4个数，因此中位数为 11。
The mode is the value that appears most often. Here 12 occurs three times, more than any other number, so the mode is 12.
众数是出现次数最多的数值。这里 12 出现了三次，比其他任何数都多，所以众数是 12。
The range shows how spread out the data is. Subtract the smallest value from the largest: 12 – 8 = 4.
范围表示数据的分散程度。用最大值减去最小值：12 – 8 = 4。
Always label each measure clearly in your answer to avoid losing communication marks.
答题时务必清晰标注每一项指标，避免因为表达不规范而丢分。
2. Mean from a Frequency Table | 根据频数表求平均数
A frequency table summarises how many books a group of 20 Year 8 pupils read in one month.
下面这个频数表汇总了 20 名 Year 8 学生在一个月内阅读的书籍数量。
| Number of books | Frequency |
|---|---|
| 0 | 2 |
| 1 | 5 |
| 2 | 8 |
| 3 | 4 |
| 4 | 1 |
To work out the mean from a frequency table, first multiply each value by its frequency and find the total of those products.
要从频数表求平均数，首先将每个数值乘上它的频数，然后算出乘积的总和。
Total books = (0 × 2) + (1 × 5) + (2 × 8) + (3 × 4) + (4 × 1) = 0 + 5 + 16 + 12 + 4 = 37. The total number of pupils is 2 + 5 + 8 + 4 + 1 = 20.
书籍总数 = (0 × 2) + (1 × 5) + (2 × 8) + (3 × 4) + (4 × 1) = 0 + 5 + 16 + 12 + 4 = 37。学生总人数为 2 + 5 + 8 + 4 + 1 = 20。
Mean = total books ÷ total frequency = 37 ÷ 20 = 1.85 books. You may leave the mean as a decimal or write it as a mixed number.
平均数 = 书籍总数 ÷ 总频数 = 37 ÷ 20 = 1.85 本。答案可以保留为小数，也可以写成带分数。
Always show the table extension in your working — adding an extra column for ‘value × frequency’ — so the examiner can see where your figures come from.
解题时务必在表格右侧增加一列“数值 × 频数”，让阅卷人清楚看到你的计算来源。
3. Interpreting a Dual Bar Chart | 解读复式条形图
A dual bar chart compares the number of boys and girls who chose each fruit as their favourite.
某复式条形图比较了选择不同水果作为最爱的男生和女生人数。
The bars show: Apple – boys 8, girls 12; Banana – boys 10, girls 7; Orange – boys 6, girls 9; Grapes – boys 11, girls 5. The question might ask, “For which fruit is the difference between boys and girls the largest?”
图中显示：苹果——男生 8 人，女生 12 人；香蕉——男生 10 人，女生 7 人；橙子——男生 6 人，女生 9 人；葡萄——男生 11 人，女生 5 人。题目可能会问：“哪一种水果的男女生人数差距最大？”
Work out the difference for each fruit: Apple |12 – 8| = 4; Banana |10 – 7| = 3; Orange |9 – 6| = 3; Grapes |11 – 5| = 6. The largest difference is 6, for grapes.
计算每种水果的差距：苹果 |12 – 8| = 4；香蕉 |10 – 7| = 3；橙子 |9 – 6| = 3；葡萄 |11 – 5| = 6。最大差距为 6，对应葡萄。
When reading dual bar charts, always check the key carefully so you know which bar represents which group. Estimate heights accurately by lining up with the gridlines.
解读复式条形图时，一定要仔细看图例，分清每一根条形代表哪一个组。借助网格线对齐高度，可以准确读出数值。
4. Pie Chart Calculations | 饼图计算
A survey asked 120 students to name their favourite sport. The results are displayed in a pie chart, where the sector for football has an angle of 90°.
一项调查询问了 120 名学生最喜爱的运动，结果用饼图展示，其中足球对应的扇形圆心角为 90°。
The number of students who chose football is found by using the fraction of the whole circle: (90°/360°) × 120 = ¼ × 120 = 30 students.
选择足球的学生人数可以用扇形圆心角占整个圆的比例来求：(90° ÷ 360°) × 120 = ¼ × 120 = 30 名学生。
If the swimming sector has an angle of 60°, then the number for swimming is (60/360) × 120 = 1/6 × 120 = 20 students. Always check that your calculated frequencies add up to the total.
如果游泳扇形的圆心角是 60°，那么喜欢游泳的人数为 (60 ÷ 360) × 120 = 1/6 × 120 = 20 人。计算完毕后，要检查各个类别人数之和是否等于总人数。
You might also be asked to draw a pie chart from a frequency table. Calculate the angle for each category as (frequency ÷ total) × 360° and use a protractor.
有时也需要根据频数表绘制饼图。此时用公式 (频数 ÷ 总数) × 360° 计算每个类别的角度，再用量角器画出扇形。
5. Line Graphs and Trend Analysis | 折线图与趋势分析
A line graph shows the temperature in a greenhouse recorded every two hours from 08:00 to 18:00: 12°C, 14°C, 17°C, 19°C, 20°C, 18°C.
某折线图展示了一个温室从 08:00 到 18:00 每隔两小时记录的温度：12°C、14°C、17°C、19°C、20°C、18°C。
To describe the trend, say: “The temperature increased steadily from 08:00 to 14:00, reaching a maximum of 20°C, then decreased slightly.” Use data values to support your description.
描述趋势时可以这样说：“温度从 08:00 到 14:00 稳步上升，最高达到 20°C，然后略有下降。”用具体数据来支持你的描述。
The greatest rise happened between 10:00 and 12:00 when the temperature went from 14°C to 17°C, an increase of 3°C.
最大升幅出现在 10:00 到 12:00 之间，温度从 14°C 上升到 17°C，升高了 3°C。
If a question asks you to predict the temperature at 20:00, the trend suggests a continued slight drop, perhaps to around 17°C. Your prediction must make sense in the context of the graph.
如果题目要求预测 20:00 的温度，根据趋势可能会继续小幅下降，大约在 17°C 左右。预测必须与图形呈现的整体走向相符。
6. Data Collection and Questionnaire Design | 数据收集与问卷设计
Good data collection is the foundation of reliable statistics. In the mock test, you might be given a flawed survey question and asked to improve it.
好的数据收集是可靠统计的基础。在模拟卷中，你可能会遇到一个设计有缺陷的调查问题，需要把它修改完善。
Original question: “Do you agree that maths is the most interesting subject and that we should have more lessons?” This is a leading and double‑barrelled question.
原问题：“你是否同意数学是最有趣的学科，而且我们应该增加课时？”这是一个带有引导性的双重问题。
An improved version would be two separate questions: “What is your favourite subject?” and “How many maths lessons per week do you think would be ideal?” The response boxes should offer clear, unbiased options.
改进后的版本可以拆成两个独立问题：“你最喜欢的学科是什么？”以及“你认为每周理想的数学课节数是多少？”选项框应当提供清晰、没有偏向的选择。
Other key design features include giving an appropriate time frame (e.g. “in the last week”) and including a full range of response choices so no one is forced to pick an inaccurate answer.
其他关键设计要素还有给出合适的时间范围（如“在过去一周内”），以及提供完整的选项范围，确保没有人被迫选择一个不准确的答案。
7. Basic Probability from Outcomes | 基于结果的简单概率
A bag contains 5 red, 3 blue and 2 green counters. One counter is taken at random. The probability of an event is (number of favourable outcomes) ÷ (total number of outcomes).
一个袋子里装有 5 个红色、3 个蓝色和 2 个绿色筹码，随机抽取一个。事件的概率等于（有利结果的数量）÷（所有可能结果的总数）。
The total number of counters is 5 + 3 + 2 = 10. The probability of picking a red counter is 5/10, which simplifies to 1/2. Probability can be written as a fraction, decimal or percentage.
筹码总数为 5 + 3 + 2 = 10。抽到红色筹码的概率是 5/10，约分为 1/2。概率可以用分数、小数或百分数表示。
Probability always lies between 0 and 1 inclusive. An event that is certain has a probability of 1; an impossible event has a probability of 0.
概率的取值永远介于 0 和 1 之间（含 0 和 1）。必然事件的概率为 1，不可能事件的概率为 0。
If the question asks “What is the probability that the counter is not blue?”, work out the complement: 1 – (3/10) = 7/10. Alternatively, add the red and green outcomes: 5 + 2 = 7 out of 10.
如果问题问“抽到的筹码不是蓝色的概率是多少？”，可以计算互补事件：1 – (3/10) = 7/10。也可以直接将红色和绿色的结果相加：5 + 2 = 7，总数为 10。
8. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph compares the daily temperature (°C) with the number of ice creams sold. Points generally rise from left to right, showing a positive correlation — as temperature increases, ice cream sales tend to increase.
某散点图将每日气温（°C）与冰淇淋销量进行比较。数据点总体上从左到右上升，表现出正相关——气温升高时，冰淇淋销量往往也会增加。
To describe correlation, use terms like ‘positive’, ‘negative’ or ‘no correlation’, and add a strength word such as ‘strong’ or ‘weak’. Always relate this back to the context.
描述相关性时，使用“正”、“负”或“无”相关，并加上表示强弱的词，如“强”或“弱”。一定要把结论和具体情境联系起来。
You may spot an outlier — a point that lies far from the general pattern. If one day with a high temperature had very low sales, it could be due to a special event or a recording error.
有时会看到一个异常点——即明显偏离整体趋势的数据点。如果某天气温很高但销量很低，可能是因为特殊活动或记录错误。
When drawing a line of best fit, it should pass through the middle of the points with roughly half above and half below. Use the line to estimate missing values but state clearly that any prediction outside the data range is unreliable.
画最佳拟合线时，这条线应通过数据点的中心，使线上下的点数大致相等。可以用这条线估算缺失值，但要明确说明超出数据范围的预测是不可靠的。
Published by TutorHao | Statistics Revision Series | aleveler.com
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